Can someone explain to me this correlation swap exercise

CAIA
#1

From Uppermark:

A correlation swap based on five assets has a notional value of $1.7 million and a strike correlation rate of 0.35. The market weights of the assets are equal. Four of the assets have realized return correlations between each other of 0.62; one of the assets has no return correlations with the other four assets. Which of the following comes closest to the net swap payment to be made to the swap buyer?

Five assets: A, B, C, D, E. Ten realized correlations: AB, AC, AD, AE, BC, BD, BE, CD, CE, DE. If one asset (say A) has no return correlations with the other assets (so remove any pairing with asset A from the list), that gives 4 zero correlations and leaves 6 non-zero correlations.

Since the asset weights are equal, the average realized correlation is: [(0.62 × 6) + (0 × 4)] / 10 = 0.372.

Swap payment = Notional value × (Avg. realized correl.− Strike correl.)

= $1.7m (0.372 − 0.35) = $37,400

Since the payment is positive, it is made to the swap buyer (by the swap seller).

This question refers to material in T7-Ch30-LO4.

My question is why do you multiple 0.62 (correlation fo 4 assets) time 6?

#2

Hi,

the multiplicator of the correlation does not mandatorily equal the number of available assets but the number of relevant correlation pairs. In this case the number of correlations pairs showing a correlation of 0.62 is 6 (using A/B/C/D/E with no correlation fo E to each other leads to following pairs with correlation of 0.62: AB - AC - AD - BC - BD - CD => 6 times correlation of 0.62 divided by total number of correlation pairs = 10)

average correlation => (6 x 0.62) / 10 = 0.372

Hope this helps

Best

#3

Hello,

Didnt know the multiplicator was used only on relevant correlation pairs.

Thanks!

#4

it’s acutally simply the arithmetic average of all possible correlation pairs within the underlying portfolio. In this case they apparently used the multiplicator to shorten it, because it’s 6 times the same number…might be a bit misleading.